$$1-7x^4-x^5 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.62944 & x_2 = 0.60223 & x_3 = -6.99958 \\[1 em] x_4 = 0.0134+0.61376i & x_5 = 0.0134-0.61376i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 1-7x^4-x^5 &= 0&& \text{simplify left side} \\[1 em]-x^5-7x^4+1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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